Plastic MFA results - consumption
Conclusion: Plastic consumption is best predicted by population and urban population after scaled log transformation
1. Relative changes over time
1.1 Consumption over time
1.2 Waste over time
1.3 Stock over time
2. Consumption vs. population
2.1 Total consumption vs. population 1950-2017
2.2 It looks like the plastic consumption of all countries grows with popluation exponentially (linearly on a log-log scale), except every country started differently in 1950. Here is a plot of plastic consumption of countries in 1950 vs. population:
log-log regression of total plastic consumption vs. population in 1950:
##
## Call:
## lm(formula = log1p(consumption[1, 7, ]) ~ log1p(socioeconomic[1,
## 1, ]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.6024 -0.5795 -0.0054 0.6270 1.8318
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.29966 0.75872 -5.667 1.39e-06 ***
## log1p(socioeconomic[1, 1, ]) 0.70699 0.08213 8.608 1.21e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9621 on 40 degrees of freedom
## Multiple R-squared: 0.6494, Adjusted R-squared: 0.6407
## F-statistic: 74.1 on 1 and 40 DF, p-value: 1.209e-10If logY = alogP + b, and logY0 = mlogP0 + n, we can get logYn = alogPn + (a-m)logP0 + (b-n). The results are not good, probably because these countries are two clusters (see above figure)
##
## Call:
## lm(formula = logYn ~ logPn + logP0, na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7448 -1.0831 0.0005 0.8385 4.4581
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.76958 0.20193 8.763 <2e-16 ***
## logPn 3.99850 0.14479 27.616 <2e-16 ***
## logP0 -0.17666 0.01981 -8.916 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.447 on 2513 degrees of freedom
## Multiple R-squared: 0.2341, Adjusted R-squared: 0.2335
## F-statistic: 384 on 2 and 2513 DF, p-value: < 2.2e-16consumption vs. pop normalized by 1950
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.8605 -0.3927 -0.0772 0.3256 5.1536
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.659e-16 1.233e-02 0.00 1
## x 7.480e-01 1.242e-02 60.21 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.659 on 2854 degrees of freedom
## Multiple R-squared: 0.5595, Adjusted R-squared: 0.5594
## F-statistic: 3626 on 1 and 2854 DF, p-value: < 2.2e-16Clustering using K-Means for two clusters
## [1] "2 clusters with size of:"## [1] 38 4## Republic of Korea Japan India
## 1 1 1
## United States of America Brazil China
## 1 1 1
## Turkey Canada Belgium
## 1 1 1
## Bulgaria Czechia Denmark
## 1 1 2
## Germany Estonia Ireland
## 1 2 2
## Greece Spain France
## 1 1 1
## Italy Cyprus Latvia
## 1 1 1
## Lithuania Luxembourg Hungary
## 1 1 1
## Malta Netherlands Austria
## 1 1 1
## Poland Portugal Romania
## 1 1 1
## Slovenia Slovakia Finland
## 2 1 1
## Sweden United Kingdom Croatia
## 1 1 1
## Iceland Norway North Macedonia
## 1 1 1
## Egypt Mexico China, Hong Kong SAR
## 1 1 1remove four outliers from clustering and plot consumption vs. pop (1950=1). There is always a small number of countries with hockystick-like curves. Standalize both consumption and population might be better. See later. Also Latvia seems to be an outlier (21)
Range between (0,1) after normalization and normalization after log. Normalization after log is better, R2 = 0.7+
##
## Call:
## lm(formula = logCspt ~ logPop, na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.50349 -0.10973 0.00066 0.08226 0.77572
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.125588 0.007099 17.69 <2e-16 ***
## logPop 0.836460 0.010722 78.02 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.16 on 2514 degrees of freedom
## Multiple R-squared: 0.7077, Adjusted R-squared: 0.7076
## F-statistic: 6086 on 1 and 2514 DF, p-value: < 2.2e-16
##
## Call:
## lm(formula = as.vector(scale(log10(consumption[, 7, ])[, -c(20,
## 23, 25, 37, 38)])) ~ as.vector(scale(log10(socioeconomic[,
## 1, ]))[, -c(20, 23, 25, 37, 38)]), na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.45757 -0.24113 -0.00673 0.19729 2.81870
##
## Coefficients:
## Estimate
## (Intercept) -1.349e-15
## as.vector(scale(log10(socioeconomic[, 1, ]))[, -c(20, 23, 25, 37, 38)]) 8.825e-01
## Std. Error
## (Intercept) 9.310e-03
## as.vector(scale(log10(socioeconomic[, 1, ]))[, -c(20, 23, 25, 37, 38)]) 9.379e-03
## t value
## (Intercept) 0.0
## as.vector(scale(log10(socioeconomic[, 1, ]))[, -c(20, 23, 25, 37, 38)]) 94.1
## Pr(>|t|)
## (Intercept) 1
## as.vector(scale(log10(socioeconomic[, 1, ]))[, -c(20, 23, 25, 37, 38)]) <2e-16
##
## (Intercept)
## as.vector(scale(log10(socioeconomic[, 1, ]))[, -c(20, 23, 25, 37, 38)]) ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.467 on 2514 degrees of freedom
## Multiple R-squared: 0.7789, Adjusted R-squared: 0.7788
## F-statistic: 8855 on 1 and 2514 DF, p-value: < 2.2e-16as shown above, normalization after log transformation seems to be able to get a good fit
2.3 By sectors (plastic consumption (kt) vs. population (1,000))
3 Total plastic consumption/person
3.1 Total plastic consumption/person vs. population in 1950:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000000 0.0001325 0.0005810 0.0010162 0.0013792 0.00538933.2 Plastic consumption/person vs. population from 1950-2017:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000000 0.002344 0.020643 0.045596 0.066930 1.0954433.3 scaled-loged plastic consumption/person vs. population from 1950-2017
##
## Call:
## lm(formula = as.vector(slogcsmpperson) ~ as.vector(slogpop),
## na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.68410 -0.26193 -0.00778 0.22293 2.87805
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.382e-15 9.760e-03 0.00 1
## as.vector(slogpop) 8.700e-01 9.832e-03 88.49 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4895 on 2514 degrees of freedom
## (340 observations deleted due to missingness)
## Multiple R-squared: 0.757, Adjusted R-squared: 0.7569
## F-statistic: 7830 on 1 and 2514 DF, p-value: < 2.2e-164. Consumption vs. GDP
nothing interesting
5. consumption vs. urbanization
5.1 consumption vs. pop after log transformation then scale
##
## Call:
## lm(formula = as.vector(slogcsmp) ~ as.vector(slogurbanpop), na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.44687 -0.17856 -0.00119 0.18494 1.73333
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.249e-16 7.073e-03 0.0 1
## as.vector(slogurbanpop) 9.340e-01 7.125e-03 131.1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3548 on 2514 degrees of freedom
## (340 observations deleted due to missingness)
## Multiple R-squared: 0.8724, Adjusted R-squared: 0.8723
## F-statistic: 1.718e+04 on 1 and 2514 DF, p-value: < 2.2e-165.2 scaled-loged consumption vs. urbanization
##
## Call:
## lm(formula = as.vector(slogcsmp) ~ as.vector(socioeconomic[,
## 6, ]), na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9827 -0.5487 0.1436 0.6226 2.1699
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.40620 0.06360 -22.11 <2e-16 ***
## as.vector(socioeconomic[, 6, ]) 2.26459 0.09824 23.05 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9022 on 2514 degrees of freedom
## (340 observations deleted due to missingness)
## Multiple R-squared: 0.1745, Adjusted R-squared: 0.1742
## F-statistic: 531.4 on 1 and 2514 DF, p-value: < 2.2e-165.3 scaled-loged consumption/person vs. urban population
##
## Call:
## lm(formula = as.vector(slogcsmpperson) ~ as.vector(slogurbanpop),
## na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.78228 -0.19990 -0.00235 0.20322 1.79857
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.742e-16 7.505e-03 0.0 1
## as.vector(slogurbanpop) 9.253e-01 7.561e-03 122.4 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3765 on 2514 degrees of freedom
## (340 observations deleted due to missingness)
## Multiple R-squared: 0.8563, Adjusted R-squared: 0.8562
## F-statistic: 1.498e+04 on 1 and 2514 DF, p-value: < 2.2e-16